If lower your FC because "now the UV is sanitizing", you won't have a FC level adequate to kill algae. UV is helpful to remove CC in indoor pools, but for an outdoor pool, the sun is already doing that. Unless you have high bather load spikes that need help in immediately oxidizing waste (which, only happens if the pump is running the whole time) then the UV doesn't do much.
You can certainly "add a puck" and use a UV system, but how much chlorine is in the pool, being added by the pucks, is dependent on your pump run time, so you'd need to test often to find that sweet spot where enough puck was being dissolved to stay ahead contaminants but not so fast as to be wasting chlorine. Plus your CYA would rise so it might be a moving target. However, CYA can naturally drift down too, so there is a potential to keep the CYA right in the same spot over time. But you'd only know by, again, testing often. And if you're trying to make life easier, that doesn't seem easier.
If you really just want to put in a "system" that runs on its own with minimal understanding of what chemical are in your pool at what levels, then ya go for it. It's quite possible that the pool will be sanitized and you'll never have algae. But you'd just be hoping and guessing. I spend 10 minutes a week testing the water and 2 minutes each night adding chemicals. I don't think it can be much easier. I could do pucks and systems to work on the pool less frequently, but not at the expense of potentially dealing with algae outbreak/shock/cloudiness/burning eyes/scaling and other mystery issues.
I had a CLear O3 oxidizer installed with my pool build, only to learn, eventually, that it does nothing but chew up my FC faster. Sunk cost.
